TSTP Solution File: FLD011-3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : FLD011-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sat Jul 16 02:26:58 EDT 2022

% Result   : Unsatisfiable 1.21s 1.41s
% Output   : Refutation 1.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   25 (  16 unt;   3 nHn;  25 RR)
%            Number of literals    :   43 (   0 equ;  22 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :   24 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(associativity_addition_1,axiom,
    ( sum(X,Y,Z)
    | ~ sum(X,U,V)
    | ~ sum(U,W,Y)
    | ~ sum(V,W,Z) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).

cnf(existence_of_identity_addition,axiom,
    ( sum(additive_identity,X,X)
    | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).

cnf(existence_of_inverse_addition,axiom,
    ( sum(additive_inverse(X),X,additive_identity)
    | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).

cnf(associativity_multiplication_1,axiom,
    ( product(X,Y,Z)
    | ~ product(X,U,V)
    | ~ product(U,W,Y)
    | ~ product(V,W,Z) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).

cnf(existence_of_identity_multiplication,axiom,
    ( product(multiplicative_identity,X,X)
    | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).

cnf(existence_of_inverse_multiplication,axiom,
    ( product(multiplicative_inverse(X),X,multiplicative_identity)
    | sum(additive_identity,X,additive_identity)
    | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).

cnf(distributivity_1,axiom,
    ( sum(X,Y,Z)
    | ~ sum(U,V,W)
    | ~ product(W,X1,Z)
    | ~ product(U,X1,X)
    | ~ product(V,X1,Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).

cnf(well_definedness_of_multiplicative_identity,axiom,
    defined(multiplicative_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).

cnf(well_definedness_of_multiplicative_inverse,axiom,
    ( defined(multiplicative_inverse(X))
    | ~ defined(X)
    | sum(additive_identity,X,additive_identity) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).

cnf(different_identities,axiom,
    ~ sum(additive_identity,additive_identity,multiplicative_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',different_identities) ).

cnf(a_is_defined,hypothesis,
    defined(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).

cnf(not_sum_2,negated_conjecture,
    ~ sum(additive_identity,a,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_2) ).

cnf(not_product_3,negated_conjecture,
    ~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_3) ).

cnf(27,plain,
    sum(additive_identity,multiplicative_identity,multiplicative_identity),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_addition,well_definedness_of_multiplicative_identity]) ).

cnf(29,plain,
    product(multiplicative_identity,a,a),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,a_is_defined]) ).

cnf(35,plain,
    sum(additive_inverse(a),a,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_addition,a_is_defined]) ).

cnf(56,plain,
    defined(multiplicative_inverse(a)),
    inference('UR-RESOLVE',[status(thm)],[well_definedness_of_multiplicative_inverse,a_is_defined,not_sum_2]) ).

cnf(82,plain,
    product(multiplicative_inverse(a),a,multiplicative_identity),
    inference('UR-RESOLVE',[status(thm)],[existence_of_inverse_multiplication,not_sum_2,a_is_defined]) ).

cnf(84,plain,
    ~ sum(additive_identity,multiplicative_identity,additive_identity),
    inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,27,different_identities,27]) ).

cnf(298,plain,
    ( product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),multiplicative_identity)
    | sum(additive_identity,multiplicative_inverse(a),additive_identity) ),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_multiplication,56]) ).

cnf(3246,plain,
    ~ sum(multiplicative_identity,a,a),
    inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,35,84,35]) ).

cnf(3295,plain,
    ~ product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),multiplicative_identity),
    inference('UR-RESOLVE',[status(thm)],[associativity_multiplication_1,82,not_product_3,29]) ).

cnf(3296,plain,
    sum(additive_identity,multiplicative_inverse(a),additive_identity),
    inference('REWRITE',[status(thm)],[298,3295]) ).

cnf(3317,plain,
    ~ sum(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity),
    inference('UR-RESOLVE',[status(thm)],[distributivity_1,3246,29,82,29]) ).

cnf(5795,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[associativity_addition_1,3296,27,27]),3317]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : FLD011-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun  6 16:59:40 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.44  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45  * 
% 0.19/0.45  * 
% 0.19/0.46  #<PACKAGE "SNARK-USER">
% 0.19/0.46  * 
% 0.19/0.46  SNARK-TPTP-OPTIONS
% 0.19/0.46  * 
% 0.19/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46   (USE-FACTORING :POS)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46  * 
% 0.19/0.46  "."
% 0.19/0.46  * 
% 0.19/0.46  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T16:59:40
% 0.19/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n019.cluster.edu at 2022-06-06T16:59:40
% 0.19/0.48  
% 0.19/0.48  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?X ?U ?V)) (NOT (|sum| ?U ?W ?Y)) (NOT (|sum| ?V ?W ?Z))).
% 0.19/0.48  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?U ?V ?X)) (NOT (|sum| ?V ?Y ?W)) (NOT (|sum| ?U ?W ?Z))).
% 0.19/0.48  ; Recognized commutativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?Y ?X ?Z))).
% 0.19/0.48  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?X ?U ?V)) (NOT (|product| ?U ?W ?Y)) (NOT (|product| ?V ?W ?Z))).
% 0.19/0.48  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?U ?V ?X)) (NOT (|product| ?V ?Y ?W)) (NOT (|product| ?U ?W ?Z))).
% 0.19/0.48  ; Recognized commutativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?Y ?X ?Z))).
% 0.19/0.48  ; Declaring sum to be commutative.
% 1.21/1.41  ; Declaring product to be commutative.
% 1.21/1.41  
% 1.21/1.41  #||
% 1.21/1.41  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.21/1.41  % SZS output start Refutation
% See solution above
% 1.21/1.41  ||#
% 1.21/1.41  
% 1.21/1.41  ; Summary of computation:
% 1.21/1.41  ;     13553 formulas have been input or derived (from 126 formulas).
% 1.21/1.41  ;      5795 (43%) were retained.  Of these,
% 1.21/1.41  ;           50 ( 1%) were simplified or subsumed later,
% 1.21/1.41  ;         5745 (99%) are still being kept.
% 1.21/1.41  ; 
% 1.21/1.41  ; Run time in seconds excluding printing time:
% 1.21/1.41  ;     0.007   1%   Read assertion file          (1 call)
% 1.21/1.41  ;     0.001   0%   Assert                       (29 calls)
% 1.21/1.41  ;     0.287  30%   Process new row              (12,669 calls)
% 1.21/1.41  ;     0.398  42%   Resolution                   (250 calls)
% 1.21/1.41  ;     0.001   0%   Paramodulation               (125 calls)
% 1.21/1.41  ;     0.000   0%   Factoring                    (3 calls)
% 1.21/1.41  ;     0.007   1%   Condensing                   (1,261 calls)
% 1.21/1.41  ;     0.050   5%   Forward subsumption          (1,261 calls)
% 1.21/1.41  ;     0.011   1%   Backward subsumption         (697 calls)
% 1.21/1.41  ;     0.006   1%   Clause clause subsumption    (2,762 calls)
% 1.21/1.41  ;     0.079   8%   Forward simplification       (12,669 calls)
% 1.21/1.41  ;     0.044   5%   Backward simplification      (5,795 calls)
% 1.21/1.41  ;     0.000   0%   Ordering                     (932 calls)
% 1.21/1.41  ;     0.000   0%   Sortal reasoning             (32 calls)
% 1.21/1.41  ;     0.000   0%   Purity testing               (1 call)
% 1.21/1.41  ;     0.059   6%   Other
% 1.21/1.41  ;     0.950        Total
% 1.21/1.41  ;     0.952        Real time
% 1.21/1.41  ; 
% 1.21/1.41  ; Term-hash-array has 8,474 terms in all.
% 1.21/1.41  ; Feature-vector-row-index has 656 entries (656 at peak, 697 added, 41 deleted).
% 1.21/1.41  ; Feature-vector-row-index has 1,543 nodes (1,543 at peak, 1,662 added, 119 deleted).
% 1.21/1.41  ;  Retrieved 2,820 possibly forward subsuming rows in 1,261 calls.
% 1.21/1.41  ;  Retrieved 750 possibly backward subsumed rows in 697 calls.
% 1.21/1.41  ; Path-index has 8,454 entries (8,454 at peak, 8,518 added, 64 deleted).
% 1.21/1.41  ; Path-index has 940 nodes (940 at peak, 953 added, 13 deleted).
% 1.21/1.41  ; Trie-index has 8,454 entries (8,454 at peak, 8,518 added, 64 deleted).
% 1.21/1.41  ; Trie-index has 24,660 nodes (24,660 at peak, 24,766 added, 106 deleted).
% 1.21/1.41  ; Retrieved 6,319 generalization terms in 13,948 calls.
% 1.21/1.41  ; Retrieved 5,235 instance terms in 5,097 calls.
% 1.21/1.41  ; Retrieved 723,715 unifiable terms in 16,707 calls.
% 1.21/1.41  ; 
% 1.21/1.41  ; The agenda of rows to process has 173 entries:
% 1.21/1.41  ;    47 with value 10             48 with value 12              18 with value 14
% 1.21/1.41  ;    41 with value 11             19 with value 13
% 1.21/1.41  ; The agenda of rows to give has 5623 entries:
% 1.21/1.41  ;     1 with value (4 8)         258 with value (4 14)         150 with value (4 20)
% 1.21/1.41  ;    17 with value (4 9)         916 with value (4 15)         644 with value (4 21)
% 1.21/1.41  ;   170 with value (4 10)         65 with value (4 16)           7 with value (4 22)
% 1.21/1.41  ;   410 with value (4 11)        446 with value (4 17)         147 with value (4 23)
% 1.21/1.41  ;   567 with value (4 12)         97 with value (4 18)           7 with value (4 25)
% 1.21/1.41  ;   912 with value (4 13)        809 with value (4 19)
% 1.21/1.41  Evaluation took:
% 1.21/1.41    0.952 seconds of real time
% 1.21/1.41    0.886109 seconds of user run time
% 1.21/1.41    0.06656 seconds of system run time
% 1.21/1.41    [Run times include 0.107 seconds GC run time.]
% 1.21/1.41    0 calls to %EVAL
% 1.21/1.41    0 page faults and
% 1.21/1.41    65,509,752 bytes consed.
% 1.21/1.41  :PROOF-FOUND
% 1.21/1.41  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T16:59:41
% 1.21/1.41  :PROOF-FOUND
% 1.21/1.41  * 
%------------------------------------------------------------------------------